# How do you simplify 2/3 + 1/5 - 1/2?

Aug 2, 2016

$\frac{11}{30}$

#### Explanation:

$\textcolor{b l u e}{\text{Considering the common denominator}}$

5 will be a factor of any number (apart from 0) that end in 5 or 10
Unfortunately a number ending with 5 can not be divided exactly by 2. So the common denominator has to be a one of the 'tens'

Note that $3 \times 10 = 30 \implies$ the common factor is 30
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$\textcolor{b l u e}{\text{Method of changing to equivalent fractions}}$

Multiply a number by 1 and you do not change its value. You can however change the way it looks.
Example: $3 \times 1 \equiv 3 \times \frac{5}{5} \equiv \frac{15}{5}$

The inherent value is still three but it looks different.
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$\textcolor{b l u e}{\text{Answering the question}}$

Write as: $\left(\frac{2}{3} \times \frac{10}{10}\right) + \left(\frac{1}{5} \times \frac{6}{6}\right) - \left(\frac{1}{2} \times \frac{15}{15}\right)$

$\left(\frac{2 \times 10}{3 \times 10}\right) + \left(\frac{1 \times 6}{5 \times 6}\right) - \left(\frac{1 \times 15}{2 \times 15}\right)$

$\frac{20}{30} + \frac{6}{30} - \frac{15}{30}$

$\textcolor{b r o w n}{\text{You can now directly add/subtract the top numbers}}$

$\frac{20 + 6 - 15}{30} = \frac{11}{30}$